The International Cycling Union, UCI, has come under fire from the independent commission it set up to investigate doping in cycling over its refusal to consider a truth and reconciliation process.

The World Anti-Doping Agency and the United States Anti-Doping Agency, the body which investigated and disclosed the misdemeanours in which Lance Armstrong was a central protagonist, believe it is imperative witnesses give evidence "without fear of retribution or retaliation from the UCI".

With the commission poised to cross-examine witnesses to establish the full extent of doping and any complicity with the UCI, Wada also expressed misgivings that much of its terms of reference relate to Armstrong, who was stripped of seven Tour de France titles and banned for life for doping.

On Tuesday Wada, Usada and Change Cycling Now, a body urging change in the governance of the sport, "informed the Commission that they would not participate in the inquiry unless the terms of reference are changed to include a truth and reconciliation process", the independent commission said on its website.

The statement added: "It is of great regret to the commission that the UCI, Wada and Usada have not been able to reach agreement to a truth and reconciliation process, and that Wada, Usada and CCN have indicated to the commission that they do not wish to participate in the inquiry on the present terms of reference.

"The commission is of the view that a truth and reconciliation process is desirable for the purposes of this inquiry, and that such a process would ensure that the most complete evidence is available to the commission at its hearing in April 2013.

"The commission is of the view that such a process would be in the interests not only of the inquiry, but also of professional cycling as a whole. The commission, via the solicitors to the inquiry, has written to the UCI's solicitors, urging the UCI to reconsider its position.

"In addition, the commission has decided to hold a procedural hearing, to take place as soon as possible after January 21, 2013, in public, where this issue will be addressed with the UCI."

The UCI is understood to be preparing a response to the independent commission, Wada and Usada. Baroness Tanni Grey-Thompson, the 11-time Paralympic champion wheelchair racer, sits on the three-person independent commission alongside the chairman, Sir Philip Otton, and Malcolm Holmes QC.

The procedural hearing will determine whether an amnesty should be enforced, the timetable of the hearing and consider the scope of the terms of reference, particularly those relating to the UCI and whether convicted dopers should have a future in the sport.

The statement added: "The commission is of the view that the participation of Usada, Wada and CCN in the inquiry would assist the commission, and it hopes that they will give further consideration to participating, and will continue to explore the possibility of a truth and reconciliation process directly with the UCI.

"The procedural hearing will be in central London, and the date, venue and time will be confirmed shortly."

Jonathan Vaughters, who, as a team-mate of Armstrong, took performance-enhancing drugs but is now boss of the Garmin-Sharp team which practices rehabilitation, welcomed the independent commission's announcement. He wrote on Twitter: "Dear UCIIC, Thank you."